1000 Solved Problems in Modern Physics

474 8 Nuclear Physics – II

The counting rate,

R=Nσνn(r) (10)

As the absorption obeys the 1/vlaw, the productσ.v=constant. We then have

250

60

= 1020 × 3 , 000 × 10 −^24 × 2. 2 × 105 n(r)

Orn(r)= 6. 313 × 10 −^5 /cm^3

Substituting the values:D= 5 × 105 ,r= 300 ,L=50 andR= 250 /60 in

(9), we find

Q= 4. 8 × 107 /s.

8.79 The absorption rate in the fuel is

ΣauφuVu

whereVis the volume, and the absorption rate in the moderator is

ΣamφmVm

The fraction of thermal neutrons absorbed by the Uranium fuel as compared

to the total number of thermal neutron absorptions in the assembly is known

as the thermal utilization factorfand is given by

f=

ΣauφuVu

ΣauφuVu+ΣamφmVm

=

1

1 +

ΣamφmVm

ΣauφuVu

Fig. 8.12 shows a unit cell of a heterogeneous assembly in which the ura-

nium rods of radiusr, are placed at regular intervals (pitch). The equivalent

cell radiusr 1 is also indicated.

Fig. 8.12Unit cell of a
heterogeneous assembly